Spheroidal 2-surfaces embedded in a time-slice of the 3+1 formalism. More...

#include <spheroid.h>

Inheritance diagram for Lorene::Spheroid:

Public Member Functions
	Spheroid (const Map_af &map, double radius)
	The delta tensorial fields linked to Christoffel symbols. More...

	Spheroid (const Scalar &h_in, const Metric &gamij, const Sym_tensor &Kij)
	Constructor of a spheroid embedded in a 3-slice (`Time_slice` ) of 3+1 formalism. More...

	Spheroid (const Spheroid &)
	Copy constructor. More...

	Spheroid (FILE *)
	Constructor from a file (see `sauve(FILE*)` ) More...

virtual	~Spheroid ()
	Destructor. More...

void	operator= (const Spheroid &)
	Assignment to another Spheroid. More...

void	set_ephi (const Scalar &)
	Assigns the conformal Killing vector field to phi. More...

const Scalar &	get_hsurf () const
	Returns the field `h_surf`. More...

const Metric &	get_qab () const
	Returns the metric $q_{ab}$ . More...

const Scalar &	get_ricci () const
	Returns the 2-ricci scalar $R = q^{ab}R_{ab}$ . More...

const Sym_tensor &	get_hh () const
	Returns the symmetric tensor $H_{ab}$ . More...

const Sym_tensor &	get_qq () const
	returns the 3-d degenerate 2-metric $Q_{ab}$ More...

const Tensor &	get_proj () const
	returns the 3-d projector on 2-surface More...

const Tensor &	get_jac2d () const
	returns the 2-d jacobian of coordinate transformation More...

const Scalar &	get_trk () const
	Returns the trace `K` on the 2-surface. More...

const Vector &	get_ll () const
	Returns the vector . More...

const Vector &	get_ss () const
	Returns the vector . More...

const Vector &	get_ephi () const
	Returns the conformal Killing symmetry vector on the 2-surface. More...

const Sym_tensor &	get_jj () const
	Returns the symmetric tensor $J_{ab}$ . More...

const Scalar &	get_fff () const
	Returns the normalization scalar `F`. More...

const Scalar &	get_ggg () const
	Returns the normalization scalar `G`. More...

bool	get_issphere () const
	Returns the flag saying whether or not the horizon is geometrically round. More...

Scalar &	set_hsurf ()
	Sets the field `h_surf`. More...

Metric &	set_qab ()
	Sets the modified metric (non degenerated) $q_{ab}$ . More...

Scalar &	set_ricci ()
	Sets the 2-Ricci scalar $R = q^{ab}R_{ab}$ . More...

Sym_tensor &	set_qq ()
	Sets the degenerated metric $Q_{ab}$ . More...

Tensor &	set_proj ()
	Sets the projector . More...

Sym_tensor &	set_hh ()
	Sets the symmetric tensor $H_{ab}$ . More...

Scalar &	set_trk ()
	Sets the trace `K` on the 2-surface. More...

Vector &	set_ll ()
	Sets the vector . More...

Vector &	set_ss ()
	Sets the vector . More...

Sym_tensor &	set_jj ()
	Sets the symmetric tensor $J_{ab}$ . More...

Scalar &	set_fff ()
	Sets the normalization factor `F`. More...

Scalar &	set_ggg ()
	Sets the normalization factor `G`. More...

bool	set_issphere ()
	Sets the boolean linked to geometrical shape of the horizon. More...

void	update_from_tslice (const Metric &gamij, const Sym_tensor &Kij)
	Updates from the 3-slice data. More...

const Scalar &	sqrt_q () const
	Computes the normal vector field to the 2-surface. More...

double	area () const
	Computes the area of the 2-surface. More...

double	angu_mom () const
	Computes the angular momentum with respect to a divergence-free vector field tangent to the 2-surface. More...

double	mass () const
	Computes the mass as defined from the calculus of angular momentum, done with respect to a divergence free tangent vector field . More...

double	multipole_mass (const int order) const
	Computes the mass multipole of a given order for the spheroid, assumed to be spherical. More...

double	multipole_angu (const int order) const
	Computes the angular multipole of a given order for the spheroid, assumed to be spherical. More...

double	epsilon_A_minus_one () const
	Computation of the refined Penrose parameter for axisymmetric spacetimes, and its difference wrt one. More...

double	epsilon_P_minus_one () const
	Computation of the classical Penrose parameter, and its difference wrt one. More...

const Scalar &	theta_plus () const
	Computes the outgoing null expansion $\theta_+$ . More...

const Scalar &	theta_minus () const
	Computes the ingoing null expansion $\theta_-$ . More...

const Sym_tensor &	shear () const
	Computes the shear of the 2-surface $\sigma_{ab}$ . More...

Tensor	derive_cov2dflat (const Tensor &uu) const
	Computes the round covariant derivative on the spheroid. More...

const Tensor &	delta () const
	Computes the delta coefficients for covariant derivative. More...

Tensor	derive_cov2d (const Tensor &uu) const
	Computes the total covariant derivative on the spheroid. More...

virtual void	sauve (FILE *) const
	Save in a file. More...

Protected Member Functions
virtual void	del_deriv () const
	Deletes all the derived quantities. More...

void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities. More...

Protected Attributes
Scalar	h_surf
	The location of the 2-surface as r = `h_surf` $(\theta, \varphi)$ . More...

Tensor	jac2d
	The jacobian of the adaptation of coordinates (contravariant/covariant representation) More...

Tensor	proj
	The 3-d projector on the 2-surface (contravariant-covariant form). More...

Sym_tensor	qq
	The 3-d covariant degenerated 2-metric on the surface. More...

Vector	ss
	The adapted normal vector field to spheroid in the 3-slice. More...

Vector	ephi
	The conformal Killing vector field on the 2-surface (set to by default to the axial vector associated with coordinate $\varphi$ ) More...

Metric	qab

Scalar	ricci
	Induced metric on the 2-surface $q_{ab}$ . More...

Sym_tensor	hh
	The ricci scalar on the 2-surface. More...

Scalar	trk
	Trace K of the extrinsic curvature of the 3-slice. More...

Vector	ll
	Normal-tangent component of the extrinsic curvature of the 3-slice. More...

Sym_tensor	jj
	Tangent components of the extrinsic curvature of the 3-slice. More...

Scalar	fff
	Normalization function for the outgoing null vector l. More...

Scalar	ggg
	Normalization function for the ingoing null vector k. More...

Scalar	zeta

bool	issphere
	Flag to know whether the horizon is geometrically round or distorted. More...

Scalar *	p_sqrt_q
	Surface element $\sqrt{\det q_{ab}}$ . More...

double *	p_area
	The area of the 2-surface. More...

double *	p_angu_mom
	The angular momentum. More...

double *	p_mass
	Mass defined from angular momentum. More...

double *	p_multipole_mass
	Mass multipole for the spheroid. More...

double *	p_multipole_angu
	Angular momentum multipole for the spheroid. More...

double *	p_epsilon_A_minus_one

double *	p_epsilon_P_minus_one
	Refined Penrose parameter, difference wrt one. More...

Scalar *	p_theta_plus
	Classical Penrose parameter, difference wrt one. More...

Scalar *	p_theta_minus
	Null ingoing expansion. More...

Sym_tensor *	p_shear
	The shear tensor. More...

Tensor *	p_delta

Friends
ostream &	operator<< (ostream &, const Spheroid &)
	Display. More...

Detailed Description

Spheroidal 2-surfaces embedded in a time-slice of the 3+1 formalism.

()

Definition at line 84 of file spheroid.h.

Constructor & Destructor Documentation

◆ Spheroid() [1/4]

Lorene::Spheroid::Spheroid	(	const Map_af &	map,
		double	radius
	)

The delta tensorial fields linked to Christoffel symbols.

Standard constructor. The input mapping must be defined on a mono-domain angular grid (see Mg3d::get_angu_mono_domain() for details).

Definition at line 97 of file spheroid.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nzone(), and Lorene::Mg3d::get_type_r().

◆ Spheroid() [2/4]

Lorene::Spheroid::Spheroid	(	const Scalar &	h_in,
		const Metric &	gamij,
		const Sym_tensor &	Kij
	)

Constructor of a spheroid embedded in a 3-slice (Time_slice ) of 3+1 formalism.

This is done from the Time_slice data.

Parameters

h_in	: the location of the surface r = h_in (WARNING:must be defined on a mono-domain angular grid)
gamij	: the 3-metric on the 3-slice
Kij	: the extrinsic curvature of the 3-slice (covariant representation)

Definition at line 153 of file spheroid.C.

◆ Spheroid() [3/4]

Lorene::Spheroid::Spheroid ( const Spheroid & sph_in )

Copy constructor.

Definition at line 594 of file spheroid.C.

References set_der_0x0().

◆ Spheroid() [4/4]

Lorene::Spheroid::Spheroid ( FILE * )

Constructor from a file (see sauve(FILE*) )

◆ ~Spheroid()

Lorene::Spheroid::~Spheroid ( )

virtual

Destructor.

Definition at line 645 of file spheroid.C.

References del_deriv().

Member Function Documentation

◆ angu_mom()

double Lorene::Spheroid::angu_mom ( ) const

Computes the angular momentum with respect to a divergence-free vector field tangent to the 2-surface.

This is defined as

${\cal J} = \int h^2 L_i \phi^i \sqrt{\det q_{ab}} \sin \theta {\rm d}\theta {\rm d}\varphi$

Parameters

phi	: the divergence-free vector field $\phi$

Definition at line 724 of file spheroid.C.

References Lorene::contract(), Lorene::Map::get_bvect_spher(), get_ephi(), Lorene::Tensor::get_mp(), h_surf, Lorene::Map_af::integrale_surface(), jac2d, ll, p_angu_mom, and sqrt_q().

◆ area()

double Lorene::Spheroid::area ( ) const

Computes the area of the 2-surface.

This is defined as

${\cal A} = \int h^2 \sqrt{\det q_{ab}} \sin \theta {\rm d}\theta {\rm d}\varphi$

Definition at line 711 of file spheroid.C.

References Lorene::Tensor::get_mp(), h_surf, Lorene::Map_af::integrale_surface(), p_area, and sqrt_q().

◆ del_deriv()

void Lorene::Spheroid::del_deriv ( ) const

protectedvirtual

Deletes all the derived quantities.

Definition at line 653 of file spheroid.C.

References p_angu_mom, p_area, p_epsilon_P_minus_one, p_mass, p_multipole_angu, p_multipole_mass, p_shear, p_sqrt_q, p_theta_minus, p_theta_plus, and set_der_0x0().

◆ delta()

const Tensor & Lorene::Spheroid::delta ( ) const

Computes the delta coefficients for covariant derivative.

Definition at line 1206 of file spheroid.C.

References Lorene::Metric::con(), Lorene::Metric::cov(), derive_cov2dflat(), Lorene::Map::get_bvect_spher(), Lorene::Metric::get_mp(), Lorene::Tensor::set(), and Lorene::Tensor::set_index_type().

◆ derive_cov2d()

Tensor Lorene::Spheroid::derive_cov2d ( const Tensor & uu ) const

Computes the total covariant derivative on the spheroid.

Definition at line 1243 of file spheroid.C.

References Lorene::contract(), delta(), derive_cov2dflat(), Lorene::Tensor::get_index_type(), and Lorene::Tensor::get_valence().

◆ derive_cov2dflat()

Tensor Lorene::Spheroid::derive_cov2dflat ( const Tensor & uu ) const

Computes the round covariant derivative on the spheroid.

Definition at line 957 of file spheroid.C.

References Lorene::Map::get_bvect_spher(), Lorene::Tensor::get_index_type(), Lorene::Tensor::get_mp(), Lorene::Tensor::get_n_comp(), Lorene::Tensor::get_triad(), Lorene::Tensor::get_valence(), Lorene::Tensor::indices(), Lorene::Itbl::set(), Lorene::Tensor::set(), Lorene::Tensor_sym::sym_index1(), and Lorene::Tensor_sym::sym_index2().

◆ epsilon_A_minus_one()

double Lorene::Spheroid::epsilon_A_minus_one ( ) const

Computation of the refined Penrose parameter for axisymmetric spacetimes, and its difference wrt one.

Definition at line 867 of file spheroid.C.

References angu_mom(), area(), mass(), Lorene::pow(), and Lorene::sqrt().

◆ epsilon_P_minus_one()

double Lorene::Spheroid::epsilon_P_minus_one ( ) const

Computation of the classical Penrose parameter, and its difference wrt one.

To use in replacement of epsilon_A_minus_one when the computed spacetime is not axisymmetric.

Definition at line 879 of file spheroid.C.

References angu_mom(), area(), mass(), p_epsilon_P_minus_one, and Lorene::pow().

◆ get_ephi()

const Vector& Lorene::Spheroid::get_ephi ( ) const

inline

Returns the conformal Killing symmetry vector on the 2-surface.

Definition at line 253 of file spheroid.h.

References ephi.

◆ get_fff()

const Scalar& Lorene::Spheroid::get_fff ( ) const

inline

Returns the normalization scalar F.

Definition at line 259 of file spheroid.h.

References fff.

◆ get_ggg()

const Scalar& Lorene::Spheroid::get_ggg ( ) const

inline

Returns the normalization scalar G.

Definition at line 262 of file spheroid.h.

References ggg.

◆ get_hh()

const Sym_tensor& Lorene::Spheroid::get_hh ( ) const

inline

Returns the symmetric tensor $H_{ab}$ .

Definition at line 232 of file spheroid.h.

References hh.

◆ get_hsurf()

const Scalar& Lorene::Spheroid::get_hsurf ( ) const

inline

Returns the field h_surf.

Definition at line 223 of file spheroid.h.

References h_surf.

◆ get_issphere()

bool Lorene::Spheroid::get_issphere ( ) const

inline

Returns the flag saying whether or not the horizon is geometrically round.

Definition at line 265 of file spheroid.h.

References issphere.

◆ get_jac2d()

const Tensor& Lorene::Spheroid::get_jac2d ( ) const

inline

returns the 2-d jacobian of coordinate transformation $ J $

Definition at line 241 of file spheroid.h.

References jac2d.

◆ get_jj()

const Sym_tensor& Lorene::Spheroid::get_jj ( ) const

inline

Returns the symmetric tensor $J_{ab}$ .

Definition at line 256 of file spheroid.h.

References jj.

◆ get_ll()

const Vector& Lorene::Spheroid::get_ll ( ) const

inline

Returns the vector $ L_a $ .

Definition at line 247 of file spheroid.h.

References ll.

◆ get_proj()

const Tensor& Lorene::Spheroid::get_proj ( ) const

inline

returns the 3-d projector on 2-surface $ Pi $

Definition at line 238 of file spheroid.h.

References proj.

◆ get_qab()

const Metric& Lorene::Spheroid::get_qab ( ) const

inline

Returns the metric $q_{ab}$ .

Definition at line 226 of file spheroid.h.

◆ get_qq()

const Sym_tensor& Lorene::Spheroid::get_qq ( ) const

inline

returns the 3-d degenerate 2-metric $Q_{ab}$

Definition at line 235 of file spheroid.h.

References qq.

◆ get_ricci()

const Scalar& Lorene::Spheroid::get_ricci ( ) const

inline

Returns the 2-ricci scalar $R = q^{ab}R_{ab}$ .

Definition at line 229 of file spheroid.h.

References ricci.

◆ get_ss()

const Vector& Lorene::Spheroid::get_ss ( ) const

inline

Returns the vector $ S_a $ .

Definition at line 250 of file spheroid.h.

References ss.

◆ get_trk()

const Scalar& Lorene::Spheroid::get_trk ( ) const

inline

Returns the trace K on the 2-surface.

Definition at line 244 of file spheroid.h.

References trk.

◆ mass()

double Lorene::Spheroid::mass ( ) const

Computes the mass as defined from the calculus of angular momentum, done with respect to a divergence free tangent vector field $ phi $ .

Spheroid has to be a real sphere (flag issphere true), of constant radius

$R_{s}$

. defined as

$M = \frac{1}{2 R_{s}} \sqrt{R_{s}^{4} + 4{\cal J}^{2}}$

Definition at line 739 of file spheroid.C.

References angu_mom(), area(), p_mass, and Lorene::sqrt().

◆ multipole_angu()

double Lorene::Spheroid::multipole_angu ( const int order ) const

Computes the angular multipole of a given order for the spheroid, assumed to be spherical.

$ phi $ is a divergence free tangent vector field. WARNING:order has to be strictly higher than zero (no topological defects here...), and an odd number for technical reasons.

Definition at line 804 of file spheroid.C.

References area(), Lorene::contract(), Lorene::Map::get_bvect_spher(), get_ephi(), Lorene::Tensor::get_mp(), h_surf, Lorene::Map_af::integrale_surface(), jac2d, ll, p_multipole_angu, Lorene::Scalar::set_spectral_va(), Lorene::sqrt(), sqrt_q(), Lorene::Scalar::std_spectral_base(), and Lorene::Valeur::ylm().

◆ multipole_mass()

double Lorene::Spheroid::multipole_mass ( const int order ) const

Computes the mass multipole of a given order for the spheroid, assumed to be spherical.

WARNING: For technical reasons, only even orders are supported by the code.

Definition at line 751 of file spheroid.C.

References area(), Lorene::Tensor::get_mp(), get_ricci(), h_surf, Lorene::Map_af::integrale_surface(), mass(), p_multipole_mass, Lorene::Scalar::set_spectral_va(), Lorene::sqrt(), sqrt_q(), Lorene::Scalar::std_spectral_base(), and Lorene::Valeur::ylm().

◆ operator=()

void Lorene::Spheroid::operator= ( const Spheroid & sph_in )

Assignment to another Spheroid.

Definition at line 617 of file spheroid.C.

References del_deriv(), ephi, fff, ggg, h_surf, hh, issphere, jac2d, jj, ll, proj, qq, ricci, ss, and trk.

◆ sauve()

void Lorene::Spheroid::sauve ( FILE * ) const

virtual

Save in a file.

Definition at line 1189 of file spheroid.C.

◆ set_der_0x0()

void Lorene::Spheroid::set_der_0x0 ( ) const

protected

Sets to 0x0 all the pointers on derived quantities.

Definition at line 669 of file spheroid.C.

References p_angu_mom, p_area, p_epsilon_P_minus_one, p_mass, p_multipole_angu, p_multipole_mass, p_shear, p_sqrt_q, p_theta_minus, and p_theta_plus.

◆ set_ephi()

void Lorene::Spheroid::set_ephi ( const Scalar & )

Assigns the conformal Killing vector field to phi.

◆ set_fff()

Scalar& Lorene::Spheroid::set_fff ( )

inline

Sets the normalization factor F.

Definition at line 298 of file spheroid.h.

References del_deriv(), and fff.

◆ set_ggg()

Scalar& Lorene::Spheroid::set_ggg ( )

inline

Sets the normalization factor G.

Definition at line 301 of file spheroid.h.

References del_deriv(), and ggg.

◆ set_hh()

Sym_tensor& Lorene::Spheroid::set_hh ( )

inline

Sets the symmetric tensor $H_{ab}$ .

Definition at line 283 of file spheroid.h.

References del_deriv(), and hh.

◆ set_hsurf()

Scalar& Lorene::Spheroid::set_hsurf ( )

inline

Sets the field h_surf.

Definition at line 268 of file spheroid.h.

References del_deriv(), and h_surf.

◆ set_issphere()

bool Lorene::Spheroid::set_issphere ( )

inline

Sets the boolean linked to geometrical shape of the horizon.

Definition at line 304 of file spheroid.h.

References del_deriv(), and issphere.

◆ set_jj()

Sym_tensor& Lorene::Spheroid::set_jj ( )

inline

Sets the symmetric tensor $J_{ab}$ .

Definition at line 295 of file spheroid.h.

References del_deriv(), and jj.

◆ set_ll()

Vector& Lorene::Spheroid::set_ll ( )

inline

Sets the vector $ L_a $ .

Definition at line 289 of file spheroid.h.

References del_deriv(), and ll.

◆ set_proj()

Tensor& Lorene::Spheroid::set_proj ( )

inline

Sets the projector $ Pi $ .

Definition at line 280 of file spheroid.h.

References del_deriv(), and proj.

◆ set_qab()

Metric& Lorene::Spheroid::set_qab ( )

inline

Sets the modified metric (non degenerated) $q_{ab}$ .

Definition at line 271 of file spheroid.h.

References del_deriv().

◆ set_qq()

Sym_tensor& Lorene::Spheroid::set_qq ( )

inline

Sets the degenerated metric $Q_{ab}$ .

Definition at line 277 of file spheroid.h.

References del_deriv(), and qq.

◆ set_ricci()

Scalar& Lorene::Spheroid::set_ricci ( )

inline

Sets the 2-Ricci scalar $R = q^{ab}R_{ab}$ .

Definition at line 274 of file spheroid.h.

References del_deriv(), and ricci.

◆ set_ss()

Vector& Lorene::Spheroid::set_ss ( )

inline

Sets the vector $ s_a $ .

Definition at line 292 of file spheroid.h.

References del_deriv(), and ss.

◆ set_trk()

Scalar& Lorene::Spheroid::set_trk ( )

inline

Sets the trace K on the 2-surface.

Definition at line 286 of file spheroid.h.

References del_deriv(), and trk.

◆ shear()

const Sym_tensor & Lorene::Spheroid::shear ( ) const

Computes the shear of the 2-surface $\sigma_{ab}$ .

Definition at line 928 of file spheroid.C.

References Lorene::Metric::cov(), fff, hh, jj, p_shear, Lorene::Tensor::std_spectral_base(), and Lorene::Tensor::trace().

◆ sqrt_q()

const Scalar & Lorene::Spheroid::sqrt_q ( ) const

Computes the normal vector field to the 2-surface.

Computes the square root of the determinant of $q_{ab}$ .

Definition at line 696 of file spheroid.C.

References get_qq(), p_sqrt_q, Lorene::sqrt(), and Lorene::Scalar::std_spectral_base().

◆ theta_minus()

const Scalar & Lorene::Spheroid::theta_minus ( ) const

Computes the ingoing null expansion $\theta_-$ .

Definition at line 912 of file spheroid.C.

References ggg, hh, jj, p_theta_minus, Lorene::Scalar::std_spectral_base(), and Lorene::Tensor::trace().

◆ theta_plus()

const Scalar & Lorene::Spheroid::theta_plus ( ) const

Computes the outgoing null expansion $\theta_+$ .

Definition at line 892 of file spheroid.C.

References fff, hh, jj, p_theta_plus, Lorene::Scalar::set_spectral_va(), Lorene::Scalar::std_spectral_base(), Lorene::Tensor::trace(), and Lorene::Valeur::ylm().

◆ update_from_tslice()

void Lorene::Spheroid::update_from_tslice	(	const Metric &	gamij,
		const Sym_tensor &	Kij
	)

Updates from the 3-slice data.

Friends And Related Function Documentation

◆ operator<<

ostream& operator<<	(	ostream &	,
		const Spheroid &
	)

friend

Display.

Member Data Documentation

◆ ephi

Vector Lorene::Spheroid::ephi

protected

The conformal Killing vector field on the 2-surface (set to by default to the axial vector associated with coordinate $\varphi$ )

Definition at line 113 of file spheroid.h.

◆ fff

Scalar Lorene::Spheroid::fff

protected

Normalization function for the outgoing null vector l.

Definition at line 138 of file spheroid.h.

◆ ggg

Scalar Lorene::Spheroid::ggg

protected

Normalization function for the ingoing null vector k.

Definition at line 143 of file spheroid.h.

◆ h_surf

Scalar Lorene::Spheroid::h_surf

protected

The location of the 2-surface as r = h_surf $(\theta, \varphi)$ .

Definition at line 91 of file spheroid.h.

◆ hh

Sym_tensor Lorene::Spheroid::hh

protected

The ricci scalar on the 2-surface.

Extrinsic curvature of the 2-surface in the 3-slice. $H_{ab}$ (covariant representation)

Definition at line 122 of file spheroid.h.

◆ issphere

bool Lorene::Spheroid::issphere

protected

Flag to know whether the horizon is geometrically round or distorted.

Definition at line 151 of file spheroid.h.

◆ jac2d

Tensor Lorene::Spheroid::jac2d

protected

The jacobian of the adaptation of coordinates (contravariant/covariant representation)

Definition at line 96 of file spheroid.h.

◆ jj

Sym_tensor Lorene::Spheroid::jj

protected

Tangent components of the extrinsic curvature of the 3-slice.

$J_{ab}$ (covariant representation)

Definition at line 134 of file spheroid.h.

◆ ll

Vector Lorene::Spheroid::ll

protected

Normal-tangent component of the extrinsic curvature of the 3-slice.

$ L_a $ (covariant representation)

Definition at line 129 of file spheroid.h.

◆ p_angu_mom

double* Lorene::Spheroid::p_angu_mom

mutableprotected

The angular momentum.

Definition at line 159 of file spheroid.h.

◆ p_area

double* Lorene::Spheroid::p_area

mutableprotected

The area of the 2-surface.

Definition at line 158 of file spheroid.h.

◆ p_epsilon_P_minus_one

double* Lorene::Spheroid::p_epsilon_P_minus_one

mutableprotected

Refined Penrose parameter, difference wrt one.

Definition at line 164 of file spheroid.h.

◆ p_mass

double* Lorene::Spheroid::p_mass

mutableprotected

Mass defined from angular momentum.

Definition at line 160 of file spheroid.h.

◆ p_multipole_angu

double* Lorene::Spheroid::p_multipole_angu

mutableprotected

Angular momentum multipole for the spheroid.

Definition at line 162 of file spheroid.h.

◆ p_multipole_mass

double* Lorene::Spheroid::p_multipole_mass

mutableprotected

Mass multipole for the spheroid.

Definition at line 161 of file spheroid.h.

◆ p_shear

Sym_tensor* Lorene::Spheroid::p_shear

mutableprotected

The shear tensor.

Definition at line 167 of file spheroid.h.

◆ p_sqrt_q

Scalar* Lorene::Spheroid::p_sqrt_q

mutableprotected

Surface element $\sqrt{\det q_{ab}}$ .

Definition at line 157 of file spheroid.h.

◆ p_theta_minus

Scalar* Lorene::Spheroid::p_theta_minus

mutableprotected

Null ingoing expansion.

Definition at line 166 of file spheroid.h.

◆ p_theta_plus

Scalar* Lorene::Spheroid::p_theta_plus

mutableprotected

Classical Penrose parameter, difference wrt one.

Null outgoing expansion

Definition at line 165 of file spheroid.h.

◆ proj

Tensor Lorene::Spheroid::proj

protected

The 3-d projector on the 2-surface (contravariant-covariant form).

Definition at line 100 of file spheroid.h.

◆ qq

Sym_tensor Lorene::Spheroid::qq

protected

The 3-d covariant degenerated 2-metric on the surface.

Definition at line 104 of file spheroid.h.

◆ ricci

Scalar Lorene::Spheroid::ricci

protected

Induced metric on the 2-surface $q_{ab}$ .

Definition at line 117 of file spheroid.h.

◆ ss

Vector Lorene::Spheroid::ss

protected

The adapted normal vector field to spheroid in the 3-slice.

Definition at line 108 of file spheroid.h.

◆ trk

Scalar Lorene::Spheroid::trk

protected

Trace K of the extrinsic curvature of the 3-slice.

Definition at line 124 of file spheroid.h.

The documentation for this class was generated from the following files:

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Spheroid() [1/4]

◆ Spheroid() [2/4]

◆ Spheroid() [3/4]

◆ Spheroid() [4/4]

◆ ~Spheroid()

Member Function Documentation

◆ angu_mom()

◆ area()

◆ del_deriv()

◆ delta()

◆ derive_cov2d()

◆ derive_cov2dflat()

◆ epsilon_A_minus_one()

◆ epsilon_P_minus_one()

◆ get_ephi()

◆ get_fff()

◆ get_ggg()

◆ get_hh()

◆ get_hsurf()

◆ get_issphere()

◆ get_jac2d()

◆ get_jj()

◆ get_ll()

◆ get_proj()

◆ get_qab()

◆ get_qq()

◆ get_ricci()

◆ get_ss()

◆ get_trk()

◆ mass()

◆ multipole_angu()

◆ multipole_mass()

◆ operator=()

◆ sauve()

◆ set_der_0x0()

◆ set_ephi()

◆ set_fff()

◆ set_ggg()

◆ set_hh()

◆ set_hsurf()

◆ set_issphere()

◆ set_jj()

◆ set_ll()

◆ set_proj()

◆ set_qab()

◆ set_qq()

◆ set_ricci()

◆ set_ss()

◆ set_trk()

◆ shear()

◆ sqrt_q()

◆ theta_minus()

◆ theta_plus()

◆ update_from_tslice()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ ephi

◆ fff

◆ ggg

◆ h_surf

◆ hh

◆ issphere

◆ jac2d

◆ jj

◆ ll

◆ p_angu_mom

◆ p_area

◆ p_epsilon_P_minus_one

◆ p_mass

◆ p_multipole_angu

◆ p_multipole_mass

◆ p_shear

◆ p_sqrt_q